Mathematical Models for Population Growth with Variable Carrying Capacity: Analytical Solutions

Abstract

A general population model with variable carrying capacity consisting of a coupled system of nonlinear ordinary differential equations is proposed, and a procedure for obtaining analytical solutions for three broad classes of models is provided. A particular case is when the population and carrying capacity per capita growth rates are proportional. As an example, a generalised Thornley–France model is given. Further examples are given when the growth rates are not proportional. A criterion when inflexion may occur is also provided, and results of numerical simulations are presented.